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Quadratic Equations Using the Vertex and Another Point

Total questions: 110

Worksheet time: 11hrs 48mins

Name
Class
Date
1.
Which of the following is vertex form of a quadratic equation?
a)
y = a(x - p)(x - q)
b)
y = a(x - h)2 - k
c)
y = a(x - h)2 + k
d)
y = a(x + h)2 + k
2.
What is the y-intercept of the equation
y = 2x2+8x+3
a)
(0,3)
b)
(3,0)
c)
(0,2)
d)
y=8
3.
Where is the AoS (Axis of Symmetry) for 
y = 2x2+4x+2
a)
x = 2
b)
x = 1
c)
x = -1
d)
x = 4
4.
Is this point a max or min?
a)
max
b)
min
5.
Find the vertex of the quadratic:
y = -2x2 + 4x + 3
a)
(0, 3)
b)
(-1, 5)
c)
(1, 5)
d)
(1, -5)
6.
What is the vertex of the graph?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)
7.
What is the vertex of y= x2 - 8x + 14 ?
a)
(2, 4)
b)
(-4, -2)
c)
(4, -2)
d)
(-2, 4)
8.

What does

x=-b/2a find?

a)

vertex

b)

y-intercept

c)

slope

d)

axis of symmetry

9.
Does the equation open or or down? 
Y = -3x2 +7x - 2
a)
up
b)
down
10.
Solve
a2 + 2a - 24 = 0
a)
a = -6, 4
b)
a = 6, -4
c)
a = 12, -2
d)
a = 8, -3
11.
What is the vertex of
f(x) = (x - 1)2 + 2?
a)
(-1, 2)
b)
(-1, -2)
c)
(1, 2)
d)
(1, -2)
12.
Which of the following equations matches standard form of a quadratic?
a)
ax + by = c
b)
y = a(x - h)2 + k
c)
y = ax2 + bx + c
d)
y = mx + b
13.
Use the graph to determine the solutions.
a)
-1 and -3
b)
1 and -3
c)
1 and 3
d)
-1 and 3
14.
How many real solutions does this quadratic have?
a)
no real solutions
b)
one solution
c)
two solutions
d)
three solutions
15.
What are the solutions for this graph?
a)
{ 0, -8}
b)
{4, 80}
c)
{0, 8}
d)
no real solution
16.
Solve the equation (x+5)(x-10)=0
a)
{5, -10}
b)
x2-5x-50
c)
{-5, 10}
d)
no solution
17.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
a)
Get factored form
b)
Write down: a=1, b=6, c=-13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
18.

No Calculator: Find the axis of symmetry and vertex.
y=−x2+10x−28y=-x^2+10x-28  

a)

Axis of Symmetry: x = 10
Vertex: (10, -28)

b)

Axis of Symmetry: x = 5
Vertex: (5, -3)

c)

Axis of Symmetry: x = -5
Vertex: (-5, -103)

d)

Axis of Symmetry: x = 5
Vertex: (5, 47)

19.

Select all the potential factors of the given graph.

a)

(x+3)

b)

(x-3)

c)

(x-8)

d)

(x+8)

e)

x

20.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
21.
What is the vertex of the parabola:
y = -12x + 22 + 2x2
a)
(3,4)
b)
(-3,4)
c)
(3, -4)
d)
(-3,-4)
22.

Solve: x2 + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

23.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
24.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
25.
Solve by factoring: 2x2 - 5x - 12 = 0
a)
x = -4 and x = -6
b)
x = 4 and x = -3/2
c)
x = 4 and x = 6
d)
x = -4 and x = 3/2
26.
If given the equation
y = 3(x + 5)2 - 4,
what is the vertex of the parabola?
a)
(5, -4)
b)
(-5, -4)
c)
(-15, -4)
d)
(15, -4)
27.

Which function has the same vertex as y = x2 + 4x - 1?

a)

y = (x - 2)2 + 5

b)

y = (x + 2)2 - 5

c)

y = (x + 2)2 - 1

d)

y = (x +2)2 + 3

28.
What's the axis of symmetry of y = 3x2 - 6x + 4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
29.
Solve
x2 + 2x - 24 = 0
a)
x = -6, x = 4
b)
x = 6, x = -4
c)
x = 12, x = -2
d)
x = 8, x = -3
30.
Solve
x2 + 9x + 20 = 0
a)
x = -2, x = -10
b)
x = -3, x = -4
c)
x = -4, x = -5
d)
x = -4, x = -6
31.
How high would you jump if the equation for jumping from a cliff is:    
h(t) = -16t2 + 8t + 24?
a)
25
b)
24
c)
8
d)
26
32.
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation 
s(t) = –16t2 + 64t + 80.
What will be the object's maximum height? 
a)
2 ft
b)
80 ft
c)
144 ft
d)
64 ft
33.
At what time would you reach 16 ft above the water if you jump of a cliff using the formula:    
h = -16t2 + 8t + 24?
a)
8
b)
1
c)
1/2
d)
1/4
34.
In order to find the vertex of an in standard form, the first two steps are to use the equation _____ to find the x value, and then you can plug that value back into the equation to find the _____.
a)
-b/2a, y-value
b)
(x-h)^2, y-intercept
c)
(x-r1), solution
d)
ax^2, vertex
35.
Find the vertex of 
f(x) = -x2 - 4x + 12.
a)
(-2, 16)
b)
(-2, 14)
c)
(2, 4)
d)
(-2, 4)
36.
a)
8 seconds
b)
2.5 seconds
c)
2.225 seconds
d)
2.5 seconds
37.
a)
24 ft
b)
8 ft
c)
12 ft
d)
10 ft
38.
a)
16 seconds
b)
10 seconds
c)
8 seconds 
d)
14 seconds
39.
a)
240 ft
b)
256 ft
c)
265 ft
d)
230 ft
40.
Determine the vertex for  y =  5x2 - 20x + 13
a)
(5, -7)
b)
(-2, -7)
c)
(2, -7)
d)
(-7, -2)
41.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x2 +600x +60

What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

42.

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t2 + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

a)

0.5 seconds

b)

1 second

c)

1.5 seconds

d)

2 seconds

e)

3 seconds

43.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t2 + 80

About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

2.24 seconds

c)

2.45 seconds

d)

2.83 seconds

44.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t2 + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

45.

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t2 + 45

When is the ball at ground level?

a)

only at t = 0 seconds

b)

only at t = 3 seconds

c)

only at t = 9 seconds

d)

at both t = 0 seconds and t = 3 seconds

46.

A lizard is jumping across the water in search of food. The equation h = -12t2 + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

0.75 seconds

e)

1 second

47.

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t2 +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

a)

2.625

b)

6.25

c)

100

d)

200

e)

210.25

48.

Your cousin hit a golf ball with an initial velocity of 27 feet per second. The equation h = -6t2 + 27t models the golf ball's height in feet t seconds after the ball was hit. How long after being hit did the ball reach maximum height?

a)

1 second

b)

2.25 seconds

c)

3 seconds

d)

4.5 seconds

e)

5 seconds

49.

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t2 + 12t. How high did the soccer ball get?

a)

1.5

b)

3

c)

5

d)

9

e)

15

50.

Which of the following mean the same as x-intercept? (More than one answer! Select all that are correct)

a)

Zero

b)

Root

c)

Axis of Symmetry

d)

Solution

e)

Maximum

51.
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation s(t) = –16t2 + 64t + 80. What will be the object's maximum height? 
a)
2 ft
b)
80 ft
c)
144 ft
d)
64 ft
52.
The function f(t) = -5t2+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? 
a)
4 seconds
b)
-2 seconds
c)
-6 seconds
d)
9 seconds
53.

The height of a water balloon that is launched into the air is given by h(t) = -5x2+20x+25. When will the balloon explode on the ground?

a)

5 seconds

b)

1 second

c)

2 seconds

d)

3 seconds

54.

The height of a water balloon that is launched into the air is given by h(t) = -5t2 + 40t + 2. From what height was the balloon released?

a)

2 meters

b)

5 meters

c)

40 meters

d)

20 meters

55.
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t2 +128t  
When will the object reach its maximum height?
a)
4 ft
b)
0 seconds
c)
0 ft
d)
4 seconds
56.
Solve the word problem:  How fast would you reach the water if you jump of a cliff using the formula:    h(t) = -16t2 + 8t + 24?
a)
8
b)
1
c)
1.5
d)
1/4
57.
A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t2 + 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?
a)
126.56 ft
b)
5.625 sec
c)
2.81 sec
d)
0 ft
58.

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t2 + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

1 second

e)

2 seconds

59.

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t2 + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

a)

1 foot

b)

5 feet

c)

7 feet

d)

8 feet

e)

12 feet

60.
What is the equation of this graph?
a)
f(x) = (x -5)2 + 1
b)
f(x) = (x - 1)2 - 5
c)
f(x) = (x + 1)2 - 5
d)
f(x) = (x + 5)2 +1
61.
If given the equation y = 3(x + 5)2 - 4, what is the vertex of the parabola?
a)
(5, -4)
b)
(-5, -4)
c)
(-15, -4)
d)
(15, -4)
62.
Identify the vertex and whether the graph opens up or down.
a)
(5, 2); opens up
b)
(5, 2); opens down
c)
(-5, 2); opens up
d)
(-5, 2); opens down
63.
A parabola has a vertex at (-3,2).
Where is the axis of symmetry?
a)
y = -2
b)
x = 3
c)
x = -3
d)
y = 2
64.
Which equation has a vertex of (-3, 4)?
a)
y = 2(x+3)2 + 4
b)
y = (x+3)2 - 4
c)
y = (x-3)2 + 4
d)
y = 2(x - 3)2 + 4
65.
What is the axis of symmetry of the given function?
a)
y = 1
b)
y = -1
c)
x = 1
d)
x = -1
66.
What is the vertex of the parabola: y=2(x-3)2+4
a)
(3,4)
b)
(-3,4)
c)
(3, -4)
d)
(-3,-4)
67.
Find the vertex.  y = x2+ 16x + 71
a)
V(-8, 7)
b)
V(-8, 3)
c)
V(8, 10)
d)
V(16, -2)
68.
Find the vertex  y = x2 - 2x - 5
a)
V(-2, 10)
b)
V(-1, 15)
c)
V(1, -6)
d)
V(1, -12)
69.

The parabola y = x2 - 2x + 4 will

a)

open up

b)

open down

70.

The parabola y = x2 - 2x + 4

a)

will have a minimum vertex.

b)

will have a maximum vertex.

71.

The parabola y = -2x2 - 4x + 1 will open

a)

up

b)

down

72.

The parabola y = x2 - 2 will

a)

open up

b)

open down

73.

The parabola y = x2 - 2 will have a vertex of

a)

(0, 2)

b)

(0, -2)

c)

(2, 0)

d)

(-2, 0)

74.

The parabola y = 3(x + 1)2 + 3 has a vertex of

a)

(3, 3)

b)

(1, 3)

c)

( - 1, 3)

d)

(3, -1)

75.

The graph of the parabola y = 3(x + 1)2 + 3

a)

will have a maximum.

b)

will have a minimum.

76.

The parabola y = 1/2(x + 4)2 - 3 will have a vertex of

a)

(4, - 3)

b)

(- 4, 3)

c)

(- 4, - 3)

d)

(4, 3)

77.
Does the graph of
-2(x + 5) + 2
have a minimum or a maximum?
a)
Minimum
b)
Maximum
c)
It has neither.
d)
It has both.
78.

Give the vertex of the equation.

a)

(1, -6)

b)

(-1, -6)

c)

(-6, 1)

d)

(1, 6)

79.

Give the vertex of the equation.

a)

(7, -206)

b)

(7, -10)

c)

(-7, -10)

d)

(-7, -206)

80.

Give the vertex of the equation.

a)

(-2, -12)

b)

(2, 12)

c)

(2, -4)

d)

(-2, -4)

81.

Give the vertex of the equation.

a)

(3, -4)

b)

(-3, 32)

c)

(-6, 5)

d)

(-3, -4)

82.

Give the vertex of the equation.

a)

(6, -4)

b)

(2, 4)

c)

(2, -4)

d)

(-2, -4)

83.

Give the vertex of the equation.

a)

(-3, -6)

b)

(-3, 6)

c)

(3, 6)

d)

(3, -6)

84.

Give the vertex of the equation.

a)

(-1, -8)

b)

(-3, 1)

c)

(3, 1)

d)

(0, 0)

85.
Find the axis of symmetry for
f(x) = x2- 8x + 15.
a)
x = -4
b)
x = 4
c)
y = 4
d)
y = -4
86.
What's the axis of symmetry of y = 3x2 - 6x + 4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
87.
Find the vertex of f(x)= -2x2-16x+3.
a)
(4, -93)
b)
(-4, 35)
c)
(-4,99)
d)
(8,3)
88.
Given y=2(x+3)(x-7), find the vertex.
a)
(2, -50)
b)
(10, 50)
c)
(-2, -18)
d)
(4, -42)
89.
Find the vertex   y = (x - 5)(x - 1)
a)
(5, 1)
b)
(-5, - 1)
c)
(3, -4)
d)
(-3, 32)
90.
What is the x-coordinate of the vertex of the parabola?
 y = (x - 8)(x + 2)
a)
3
b)
-3
c)
8 and -2
d)
-8 and 2
91.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
92.
Solve the following quadratic.
x2 - x - 20 = 0
a)
x = -5  x = 4
b)
x = -10  x = 2
c)
x = 5  x = -4
d)
x = 10  x = -2
93.
Solve the following quadratic.
2x2 - 11x + 5 = 0
a)
x = 1/2  x = 5
b)
x = 1  x = 5/2
c)
x = -1  x = -5/2
d)
x = -1/2  x = -5
94.
Solve the following quadratic.
6x2 + x = 1
a)
x = 3  x = -2
b)
x = -3  x = 2
c)
x = -1/3  x = 1/2
d)
x = 1/3  x = -1/2
95.
What is the y-intercept for the following quadratic?
y = -5x2 - 12 + 4x
a)
y = 4
b)
y = -12
c)
y = -5
d)
y = -4
96.
Solving the following quadratic.
4x2 + 9x + 5 = 0
a)
(5/4, 1)
b)
(-1/4, -5)
c)
(-5/4, -1)
d)
(1/4, 5)
97.
Which answer choice describes  y = -3x2 +7x - 2 accurately?
a)
opens up with a maximum
b)
opens up with a minimum
c)
opens down with a maximum
d)
opens down with a minimum 
98.
What is the first step when factoring polynomials?
a)
Find the GCF
b)
List all the terms
c)
Make a triangle
d)
Write the answer
99.
Factor completely:
 3x² + 5x - 12
a)
(3x + 4)(x-3)
b)
(3x - 4)(x + 3)
c)
(3x + 3)(x -4)
d)
(3x - 3)(x + 4)
100.
Factor completely: 3x2-8x+4
a)
(3x-4)(x-1)
b)
(3x-2)(x-2)
c)
(x+1)(3x+4)
d)
(x+2)(3x+2)
101.
Solve
a2 + 2a - 24 = 0
a)
a = -6, 4
b)
a = 6, -4
c)
a = 12, -2
d)
a = 8, -3
102.
Solve for m by factoring.
a)
A
b)
B
c)
C
d)
D
103.
Solve for v by factoring.
a)
A
b)
B
c)
C
d)
D
104.
Solve for x by factoring.
a)
-6, -2
b)
-2, 6
c)
2, 6
d)
-6, 2
105.
Solve for v by factoring. 
*Remember the equation must equal 0*
a)
A
b)
B
c)
C
d)
D
106.
Solve for n by factoring.
a)
-4, 2
b)
-2, 4
c)
-16
d)
-4
107.
Factor out the GCF:
12x + 6
a)
6(2x + 1)
b)
3(4x + 2)
c)
6x(2x + 1)
d)
2(6x + 3)
108.
What are the values of x when y = 0?
a)
{ -3, 1 }
b)
{ -2 }
c)
{ -3, -1 }
d)
{ 1, 3 }
109.
a)
-3, 4
b)
3, 4
c)
-4, -3
d)
-3
110.
a)
-6, -2
b)
-2, 6
c)
2, 6
d)
-6, 2

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Algebra OST Review

106 questions

Algebra OST Review

quiz

Worksheet

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9th - 12th Grade

Exponential Functions Review

105 questions

Exponential Functions Review

quiz

Worksheet

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9th - 12th Grade